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3 years ago

What is the simplified form of (4x^2y^3)^3?

Mathematics

1 answer:

levacccp [35]3 years ago

7 0

Answer:

Step-by-step explanation:

(4x² 2y³)³ = 64x⁵y⁶

4x4x4 = 64

(x²)³ = x⁵

(y³)³ = y⁶

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Expand the given power using the Binomial Theorem. (10k – m)5

agasfer [191]

Answer:

$(10k - m)^{5}=100000k-50000k^{4}m+10000k^{3}m^{2}-1000k^{2}m^{3}+50km^{4}-m^{5}$

Step-by-step explanation:

* Lets explain how to solve the problem

- The rule of expand the binomial is:

$(a+b)^{n}=(a)^{n}+nC1(a)^{n-1}(b)+nC2(a)^{n-2}(b)^{2}+nC3(a)^{n-3}(b)^{3}+...............+(b)^{5}$

∵ The binomial is $(10k-m)^{5}$

∴ a = 10k , b = -m and n = 5

∴ $(10k-m)^{5}=(10k)^{5}+5C1(10k)^{4}(-m)+5C2(10k)^{3}(-m)^{2}+5C3(10k)^{2}(-m)^{3}+5C4(10k)^{1} (-m)^{4}+5C5(10k)^{0}(-m)^{5}$

∵ 5C1 = 5

∵ 5C2 = 10

∵ 5C3 = 10

∵ 5C4 = 5

∵ 5C5 = 1

∴ $(10k-m)^{5}=100000k^{5}+(5)(10000)k^{4}(-m)+(10)(1000)k^{3}(m^{2})+(10)(100)k^{2}(-m^{3})+5(10k)^{1} (m^{4})+(10k)^{0}(-m^{5})$

∴ $(10k-m)^{5}=100000k^{5}-50000)k^{4}m+10000k^{3}m^{2}-1000k^{2}m^{3}+50km^{4}-m^{5}$

5 0

3 years ago

If (a−8)/3=(a−3)/2 , then a = ?

Tresset [83]

Answer:

$\frac{(a - 8)}{3} = \frac{(a - 3)}{2} \\ 2(a - 8) = 3(a - 3) \\ 2a - 16 = 3a - 9 \\ 3a - 2a = - 7 \\ a = - 7$

4 0

3 years ago

Read 2 more answers

Two 6-sided dice are rolled at the same time. How many outcomes correspond to the event that the sum of the numbers is 5?

katen-ka-za [31]

Well I don't know !
Let's count them.

You can get a 5 if the cubes
fall in any one of these ways:

1 . . . 4
2 . . . 3
3 . . . 2
4 . . . 1

That looks like four possibilities.
Can you think of any others that I missed ?

3 0

4 years ago

A = 8: b = ; C = 10.

lara [203]

Answer:

b=6

$a^{2} + b^{2} = c^{2} \\ {8}^{2} + {b}^{2} = {10}^{2} \\ 64 + {b}^{2} = 100 \\ 100 - 64 = {b}^{2} \\ 36 = {b}^{2} \\ \sqrt{36} = \sqrt{ {b}^{2} } \\ 6 = b$

8 0

3 years ago

A farmer is tracking the number of soybeans his land is yielding each year. He finds that the function f(x) = −x2 + 20x + 100 mo

Aliun [14]

Answer:

The average rate of change = -10

The crop yield decreased by 10 pounds per acre from year 10 to year 20.

Step-by-step explanation:

A farmer is tracking the number of soybeans his land is yielding each year. He finds that the function $f(x) =-x^2 + 20x + 100$ models the crops in pounds per acre over x years.